Rupp, R. and Sasane, Amol 
ORCID: 0000-0001-5566-9877
(2010)
On the stable rank and reducibility in algebras of real symmetric functions.
Mathematische Nachrichten, 283 (8).
pp. 1194-1206.
ISSN 0025-584X
Abstract
Let Aℝ([MATHEMATICAL DOUBLE-STRUCK CAPITAL D]) denote the set of functions belonging to the disc algebra having real Fourier coefficients. We show that Aℝ([MATHEMATICAL DOUBLE-STRUCK CAPITAL D]) has Bass and topological stable ranks equal to 2, which settles the conjecture made by Brett Wick in [18]. We also give a necessary and sufficient condition for reducibility in some real algebras of functions on symmetric domains with holes, which is a generalization of the main theorem in [18]. A sufficient topological condition on the symmetric open set [MATHEMATICAL DOUBLE-STRUCK CAPITAL D] is given for the corresponding real algebra Aℝ([MATHEMATICAL DOUBLE-STRUCK CAPITAL D]) to have Bass stable rank equal to 1.
| Item Type: | Article |
|---|---|
| Official URL: | http://www.wiley-vch.de/publish/en/journals/alphab... |
| Additional Information: | © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 28 Jul 2011 09:17 |
| Last Modified: | 11 Dec 2024 23:47 |
| URI: | http://eprints.lse.ac.uk/id/eprint/37643 |
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